Lithographic apparatus and device manufacturing method utilizing data filtering

ABSTRACT

An apparatus and method are used to form patterns on a substrate. The apparatus comprises a projection system, a patterning device, a low-pass filter, and a data manipulation device. The projection system projects a beam of radiation onto the substrate as an array of sub-beams. The patterning device modulates the sub-beams to substantially produce a requested dose pattern on the substrate. The low-pass filter operates on pattern data derived from the requested dose pattern in order to form a frequency-clipped target dose pattern that comprises only spatial frequency components below a selected threshold frequency. The data manipulation device produces a control signal comprising spot exposure intensities to be produced by the patterning device, based on a direct algebraic least-squares fit of the spot exposure intensities to the frequency-clipped target dose pattern. In various examples, filters can also be used.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional of U.S. patent application Ser. No.12/166,837, now U.S. Pat. No. 7,864,295, filed Jul. 2, 2008, which is aDivisional of U.S. patent application Ser. No. 11/093,259, now U.S. Pat.No. 7,403,265, filed on Mar. 30, 2005, the disclosures of which areincorporated herein by reference in their entireties.

BACKGROUND

1. Field

The present invention relates to a lithographic apparatus and a methodfor manufacturing a device.

2. Related Art

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture offlat panel displays, integrated circuits (ICs),micro-electro-mechanical-systems (MEMS), and other devices involvingfine structures. In a conventional apparatus, a contrast device or apatterning device, which can be referred to as a mask or a reticle, canbe used to generate a circuit pattern corresponding to an individuallayer of a flat panel display or other device. This pattern can betransferred onto a target portion (e.g., comprising part of one orseveral dies) on a substrate (e.g., a glass plate). Transfer of thepattern is typically via imaging onto a layer of radiation-sensitivematerial (e.g., resist) provided on the substrate.

Instead of a circuit pattern, the patterning device can be used togenerate other patterns, for example a color filter pattern or a matrixof dots. Instead of a mask, the patterning device can comprise apatterning array that comprises an array of individually controllableelements. Compared to a mask-based system, the pattern can be changedmore quickly and for less cost.

In general, a flat panel display substrate is rectangular in shape.Known lithographic apparatus designed to expose a substrate of this typetypically provide an exposure region, which covers a full width of therectangular substrate, or which covers a portion of the width (e.g.,about half of the width). The substrate is scanned underneath theexposure region, while the mask or reticle is synchronously scannedthrough the beam. In this way, the pattern is transferred to thesubstrate. If the exposure region covers the full width of thesubstrate, then exposure is completed with a single scan. If theexposure region covers, for example, half of the width of the substrate,then the substrate is moved transversely after the first scan, and asecond scan is performed to expose the remainder of the substrate.

Another way of imaging includes pixel grid imaging, in which a patternis realized by successive exposure of spots.

Where the pattern on the substrate is built up from a grid of localizedexposures or “spot exposures,” it is found that the quality of thepattern formed at a particular point can depend on where that point islocated relative to the spot exposure grid positions. Furthermore, avariation in pattern quality can be found to exist with respect to theangle of a feature in the pattern relative to axes defining the grid.Either or both of these variations can have a negative influence on thequality of a device to be manufactured.

The image log slope of a pattern determines the resist side-wall angleof features formed after processing of an exposed substrate. A shallowimage log slope implies a shallow side wall angle, which can be useful,for example, for achieving a wide viewing angle for Flat Panel Displaysor can reduce the consequences of overlay errors. Steeper image logslopes and side wall angles provide greater contrast. The maximal imagelog slope is determined by the point spread functions of the spotexposures in the grid, and on the geometrical properties of the grid. Ingeneral, therefore, the image log slope is fixed once the correspondinghardware elements have been finalized. However, it can be desirable tovary the image log slope according to the nature of the application.

The critical dimension (CD) refers to the size of the smallest printablefeature. Although the CD of the dose pattern can be defined quiteaccurately prior to exposure, it is more difficult to predict the CDproperties of the pattern after post-exposure processing. Frequently, itis desirable to tweak the CD after inspection of a processed substratein order to optimize the processed pattern according to a customer'srequirements. One way this can be achieved is to vary the intensity ofthe radiation source. The more intense it is, the more the resultingpattern is spread out (normally leading to an increased CD). However, CDbiasing in this way can only be applied uniformly and in a circularlysymmetrical fashion over the surface of the substrate.

Variation in the position of the substrate surface relative to the planeof best focus can cause deterioration in the quality of the image formedon the substrate. Complex servo and control systems can be provided totranslate and/or tilt the substrate table and/or projection system inorder to keep the substrate near the plane of best focus but it isdifficult to achieve perfect compensation. A residual focus error tendsto remain.

Where an array of individually controllable elements is used as apatterning device, some form of conversion tool is to translaterequested spot exposure doses to voltages suitable for actuating thecorresponding elements of the array at the appropriate times. Forexample, where the array of individually controllable elements comprisesa mirror array, the voltages will be chosen so as to cause individualmirrors or groups of mirrors to tilt in such a way as to deflect anappropriate portion of incident radiation through the projection system.The relationship between the proportion of deflected radiation and thevoltage/tilt angle can be complex (e.g., non-linear). Factors thataffect the intensity/uniformity of the radiation incident on the arrayof individually controllable elements and variations in the opticalproperties of projection system components (e.g., variations betweendifferent optical columns) can also affect the intensity of radiationreaching the substrate and thereby reduce the quality of the patternformed.

Where an array of individually controllable elements is used as apatterning device, ghost light (i.e., light originating from elementsother than those that are supposed to be contributing to a particularsub-beam of radiation) can cause errors in the pattern formed on thesubstrate.

Therefore, what is needed is a system and method that more efficientlyand effectively performs maskless lithography.

SUMMARY

According to one embodiment of the present invention, there is provideda lithographic apparatus comprising a projection system, a patterningdevice, a low pass filter, and a data manipulation device. Theprojection system projects a beam of radiation onto a substrate as anarray of sub-beams of radiation. The patterning device modulates thesub-beams of radiation to substantially produce a requested dose patternon the substrate. The dose pattern is built up from an array of spotexposures in which at least neighboring spot exposures are imagedincoherently with respect to each other and each spot exposure isproduced by one of the sub-beams of radiation at a particular time. Thelow-pass filter is arranged to operate on pattern data derived from therequested dose pattern in order to form a frequency-clipped target dosepattern that predominantly comprises only spatial frequency componentsbelow a selected threshold frequency. The data manipulation deviceproduces a control signal comprising spot exposure intensities to beproduced by the patterning device, based on a direct algebraicleast-squares fit of the spot exposure intensities to thefrequency-clipped target dose pattern.

According to one embodiment of the present invention, there is provideda lithography apparatus comprising a projection system, a patterningdevice, a data manipulation device, and a low pass filter. Theprojection system projects a beam of radiation onto a substrate as anarray of sub-beams of radiation. The patterning device modulates thesub-beams of radiation in order substantially to produce a requesteddose pattern on the substrate. The dose pattern is built up from anarray of spot exposures in which at least neighboring spot exposures areimaged incoherently with respect to each other and each spot exposure isproduced by one of the sub-beams of radiation at a particular time. Thedata manipulation device produces a control signal comprising spotexposure intensities to be produced by the patterning device. Thecontrol signal is based on a direct algebraic least-squares fit of thespot exposure intensities to data derived from the requested dosepattern. The least-squares fit is performed by multiplying apseudo-inverted form of a point-spread function matrix by a columnvector representing the pattern data derived from the requested dosepattern, the point-spread function matrix comprising information aboutthe shape and relative position of the point-spread function of eachspot to be exposed on the substrate by one of the sub-beams of radiationat a given time. The low-pass filter removes spatial frequencycomponents of a signal above a selected threshold frequency,incorporated offline into the pseudo-inverted form of thepoint-spread-function matrix, ready for the least-squares fit, by thefollowing operation:[K] ⁺ _(filtered) =F _(low-pass filter)

[K] ⁺,

where [K]⁺ and [K]⁺ _(filtered) represent the pseudo-inverted form ofthe point-spread function matrix respectively before and afterfiltering, and where F_(low-pass filter) represents a mathematicaldefinition of the low-pass filter in the spatial domain.

According to one embodiment of the present invention, there is provideda lithography apparatus comprising a projection system, an array ofindividually controllable elements, a rasterizer device, a datamanipulation device, and a focus determination unit. The projectionsystem projects a beam of radiation onto a substrate as an array ofsub-beams of radiation. The array of individually controllable elementsmodulates the sub-beams of radiation so as substantially to form arequested dose pattern on the substrate, the requested dose patternbeing built up over time from an array of spot exposures, each spotexposure being produced by one of the sub-beams of radiation at a giventime. The rasterizer device converts data defining the requested dosepattern to a sequence of data representing the requested dose at acorresponding sequence of points within the pattern. The datamanipulation device receives the sequence of data and generates acontrol signal therefrom suitable for controlling the array ofindividually controllable elements. The focus determination unitmeasures the position of at least a portion of the substrate relative toa plane of best focus. The data manipulation device comprises a focuscompensation unit that adapts the control signal based on measureddeviations of the at least a portion of the substrate relative to theplane of best focus.

According to one embodiment of the present invention, there is provideda lithography apparatus comprising a patterning device, a projectionsystem, and a CD-biasing filter. The patterning device modulates a beamof radiation. The projection system projects the modulated beam ofradiation onto a substrate. The CD-biasing filter operates on patterndata derived from a requested dose pattern, which is to be fed to thepatterning device, in order to control the critical dimensioncharacteristics of a radiation dose pattern produced by the patterningdevice.

According to one embodiment of the present invention, there is provideda lithography apparatus comprising an illumination system, a projectionsystem, a patterning device, and a data manipulation device. Theillumination system conditions a beam of radiation. The projectionsystem projects the beam of radiation onto the substrate as an array ofsub-beams of radiation. The patterning device modulates the sub-beams ofradiation to substantially produce a requested dose pattern on thesubstrate. The dose pattern is built up from an array of spot exposures,each spot exposure being produced by one of the sub-beams of radiationat a particular time. The radiation intensity of a given sub-beam ofradiation is controlled according to an activation state of acorresponding portion of the patterning device. The data manipulationdevice transforms a signal comprising spot exposure radiation dosesderived from the requested dose pattern to a control signal representingactivation states of the patterning device substantially to produce therequested dose pattern. The transformation is adapted in order tocorrect for intensity variations caused by at least one of thefollowing: components of the projection system, components of theillumination system, radiation sources for the illumination system, andcomponents of the patterning device.

According to one embodiment of the present invention, there is provideda device manufacturing method comprising the following steps. Providinga projection system to project a beam of radiation onto a substrate asan array of sub-beams of radiation. Providing a patterning device thatmodulates the sub-beams of radiation to substantially produce arequested dose pattern on the substrate. The dose pattern is built upfrom an array of spot exposures in which at least neighboring spotexposures are imaged incoherently with respect to each other and eachspot exposure is produced by one of the sub-beams of radiation at aparticular time. Using a low-pass filter to operate on pattern dataderived from the requested dose pattern in order to form afrequency-clipped target dose pattern that comprises only spatialfrequency components below a selected threshold frequency. Using a datamanipulation device to produce a control signal comprising spot exposureintensities to be produced by the patterning device, based on a directalgebraic least-squares fit of the spot exposure intensities to thefrequency-clipped target dose pattern.

According to one embodiment of the present invention, there is provideda device manufacturing method comprising the following steps. Providinga projection system that projects a beam of radiation onto a substrateas an array of sub-beams of radiation. Providing a patterning devicethat modulates the sub-beams of radiation in order substantially toproduce a requested dose pattern on the substrate. The dose pattern isbuilt up from an array of spot exposures in which at least neighboringspot exposures are imaged incoherently with respect to each other andeach spot exposure is produced by one of the sub-beams of radiation at aparticular time. Using a data manipulation device to produce a controlsignal comprising spot exposure intensities to be produced by thepatterning device, based on a direct algebraic least-squares fit of thespot exposure intensities to data derived from the requested dosepattern, wherein the least-squares fit is performed by multiplying apseudo-inverted form of a point-spread function matrix by a columnvector representing the pattern data derived from the requested dosepattern, the point-spread function matrix comprising information aboutthe shape and relative position of the point-spread function of eachspot to be exposed on the substrate by one of the sub-beams of radiationat a given time. Using a low-pass filter to remove spatial frequencycomponents of a signal above a selected threshold frequency,incorporated offline into the pseudo-inverted form of thepoint-spread-function matrix, ready for the least-squares fit, by thefollowing operation: [K]⁺ _(filtered)=F_(low-pass filter)

[K]⁺, where [K]⁺ and [K]⁺ _(filtered) represent the pseudo-inverted formof the point-spread function matrix respectively before and afterfiltering, and where F_(low-pass filter) represents a mathematicaldefinition of the low-pass filter in the spatial domain.

According to one embodiment of the present invention, there is a devicemanufacturing method comprising the following steps. Providing aprojection system that projects a beam of radiation onto a substrate asan array of sub-beams of radiation. Providing an array of individuallycontrollable elements that modulate the sub-beams of radiation so assubstantially to form a requested dose pattern on the substrate. Therequested dose pattern is built up over time from an array of spotexposures, each spot exposure being produced by one of the sub-beams ofradiation at a given time. Providing a rasterizer device that convertsdata defining the requested dose pattern to a sequence of datarepresenting the requested dose at a corresponding sequence of pointswithin the pattern. Using a data manipulation device to receive thesequence of data and generate a control signal therefrom suitable forcontrolling the array of individually controllable elements. Using afocus determination unit to measure the position of at least a portionof the substrate relative to a plane of best focus. Using a focuscompensation unit to adapt the control signal based on measureddeviations of the at least a portion of the substrate relative to theplane of best focus.

According to one embodiment of the present invention, there is provideda device manufacturing method comprising the following steps. Providinga patterning device that modulates a beam of radiation. Providing aprojection system that projects the modulated beam of radiation onto asubstrate. Using a CD-biasing filter to operate on pattern data derivedfrom a requested dose pattern, which is to be fed to the patterningdevice, in order to control the critical dimension characteristics of aradiation dose pattern produced by the patterning device.

According to one embodiment of the invention, there is a devicemanufacturing method comprising the following steps. Providing anillumination system that conditions a beam of radiation. Providing aprojection system that projects the beam of radiation onto the substrateas an array of sub-beams of radiation. Providing a patterning devicethat modulates the sub-beams of radiation to substantially produce arequested dose pattern on the substrate. The dose pattern is built upfrom an array of spot exposures, each spot exposure being produced byone of the sub-beams of radiation at a particular time. The radiationintensity of a given sub-beam of radiation is controlled according to anactivation state of a corresponding portion of the patterning device.Using a data manipulation device to transform a signal comprising spotexposure radiation doses derived from the requested dose pattern to acontrol signal representing activation states of the patterning devicesubstantially to produce the requested dose pattern. Adapting thetransformation to correct for intensity variations caused by at leastone of the following: components of the projection system, components ofthe illumination system, radiation sources for the illumination system,and components of the patterning device.

Further embodiments, features, and advantages of the present inventions,as well as the structure and operation of the various embodiments of thepresent invention, are described in detail below with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and foam a partof the specification, illustrate one or more embodiments of the presentinvention and, together with the description, further serve to explainthe principles of the one or more embodiments of the present inventionand to enable a person skilled in the pertinent art to make and use theone or more embodiments of the present invention.

FIG. 1 depicts a lithographic apparatus, according to one embodiment ofthe present invention.

FIG. 2 depicts a lithographic apparatus that can be used, for example,in the manufacture of a flat panel display, according to one embodimentof the present invention.

FIG. 3 depicts a mode of transferring a pattern to a substrate using alithographic apparatus, according to one embodiment of the presentinvention.

FIG. 4 depicts an arrangement of optical engines for exposing a patternon a substrate, for example, used to manufacture a flat panel display,according to one embodiment of the present invention.

FIG. 5 depicts a data-path with data manipulation devices, according toone embodiment of the present invention.

FIG. 6 depicts a portion of a square spot exposure grid and a “worstcase” position, according to one embodiment of the present invention.

FIG. 7 depicts a portion of a hexagonal spot exposure grid and a “worstcase” position, according to one embodiment of the present invention.

FIG. 8 depicts a portion of a square spot exposure grid with “worstcase” lines and “best case” positions, according to one embodiment ofthe present invention.

FIG. 9 depicts a portion of a hexagonal spot exposure grid with “worstcase” positions and “best case” positions, according to one embodimentof the present invention.

FIG. 10 depicts the hexagonal spot exposure grid geometry and shows an“intermediate case” position, according to one embodiment of the presentinvention.

FIG. 11 depicts a low-pass and sharpening combination filter, accordingto one embodiment of the present invention.

FIG. 12 depicts an image log slope filter, according to one embodimentof the present invention.

FIG. 13 depicts a CD biasing filter, according to one embodiment of thepresent invention.

FIG. 14 depicts an apparatus suitable for on-the-fly focus correctionvia a data-path, according to one embodiment of the present invention.

FIG. 15 depicts a multiplication stage with a preprocessor for reducingcalculation load, according to one embodiment of the present invention.

The present invention will now be described with reference to theaccompanying drawings. In the drawings, like reference numbers canindicate identical or functionally similar elements.

DETAILED DESCRIPTION

In one embodiment of the present invention provides a blazing portion ina section of an array of individually controllable elements (e.g., acontrast device). All the elements in the blazing portion have theirindividually controllable elements positioned at a same angle, whichforms the blazing portion. In one example, this can be accomplishedthrough use of a super-pixel. The blazing portion is used to increaselight intensity in a first diffraction order a beam modulated by thearray. This is accomplished by substantially eliminating a negativefirst diffraction order modulated beam, such that the positive firstdiffraction order modulated beam has, in effect, about equal to or morethan twice the intensity compared to a typical positive firstdiffraction order modulated beam. For example, when using a λ/4 tipdeflection, substantially all of the incident light is reflected in thefirst diffraction order.

In another embodiment, instead of a first diffraction order, a higherdiffraction order can be used by higher tip deflection. For instance,all the light is concentrated in the second diffraction order for λ/2tip deflection. It is to be appreciated that all the light isconcentrated in the n-th diffraction order upon n times λ/4 tipdeflection.

In another embodiment, perpendicular projection is accomplished bydirecting light onto the array at a diffraction order of interest (whichis used within the projection part), where the light can also impinge ona blazing portion of the array, such that the projected light leaves thecontrast device perpendicular.

Thus, in one example, through use of a blazing portion it is possible toconcentrate substantially all of the diffracted energy in the order ofinterest (e.g., a diffraction order) towards a substrate.

In another embodiment, “partial coherent imaging” mode can be used,during which the array of individually controllable elements is imagedat the substrate, however no super-pixels are used.

Overview And Terminology

The use of “object,” “substrate,” “work piece,” or the like areinterchangeable in this application, and can be, but are not limited to,a work piece, a substrate (e.g., a flat panel display glass substrate),a wafer (e.g., a semiconductor wafer for integrated circuitmanufacture), a print head, micro or nano-fluidic devices, a displaypanel in a projection display system, or the like.

The terms “contrast device,” “patterning device,” “patterning array,” or“array of individually controllable elements” used herein should bebroadly interpreted as referring to any device that can be used tomodulate the cross-section of a radiation beam such as to create apattern in a target portion of a substrate (e.g., object). It should benoted that the pattern imparted to the radiation beam may not exactlycorrespond to the desired pattern in the target portion of thesubstrate, for example if the pattern includes phase-shifting featuresor so called assist features. Similarly, the pattern eventuallygenerated on the substrate may not correspond to the pattern formed atany one instant on the array of individually controllable elements. Thiscan be the case in an arrangement in which the eventual pattern formedon each part of the substrate is built up over a given period of time ora given number of exposures during which the pattern on the array ofindividually controllable elements and/or the relative position of thesubstrate changes. Generally, the pattern created on the target portionof the substrate will correspond to a particular functional layer in adevice being created in the target portion, such as an integratedcircuit. The terms “light valve” and “Spatial Light Modulator” (SLM) canalso be used in this context. Examples of such patterning devicesinclude:

A programmable mirror array. This can comprise a matrix-addressablesurface having a viscoelastic (e.g., having viscous as well as elasticproperties) control layer and a reflective surface. The basic principlebehind such an apparatus is that, for example, addressed areas of thereflective surface reflect incident light as diffracted light, whereasunaddressed areas reflect incident light as undiffracted light. Using anappropriate spatial filter, the undiffracted light can be filtered outof the reflected beam, leaving only the diffracted light to reach thesubstrate. In this manner, the beam becomes patterned according to theaddressing pattern of the addressable surface.

It will be appreciated that, as an alternative, the filter can filterout the diffracted light, leaving the undiffracted light to reach thesubstrate.

An array of diffractive optical MEMS devices (Micro Electro-MechanicalSystems) can also be used in a corresponding manner. Each diffractiveoptical MEMS device is comprised of a plurality of reflective ribbonsthat can be deformed relative to one another to form a grating thatreflects incident light as diffracted light.

A further alternative embodiment of a programmable mirror array employsa matrix arrangement of tiny mirrors, each of which can be individuallytilted about an axis by applying a suitable localized electric field, orby employing piezoelectric actuation means. Once again, the mirrors arematrix-addressable, such that addressed mirrors will reflect an incomingradiation beam in a different direction to unaddressed mirrors; in thismanner, the reflected beam is patterned according to the addressingpattern of the matrix-addressable mirrors. The matrix addressing can beperformed using suitable electronic means. Mirror arrays are describedin, for example, U.S. Pat. Nos. 5,296,891 and 5,523,193, and PCT patentapplications WO 98/38597 and WO 98/33096, which are incorporated hereinby reference in their entireties.

The lithographic apparatus can comprise one or more patterning arrays.For example, it can have a plurality of arrays of individuallycontrollable elements, each controlled independently of each other. Insuch an arrangement, some or all of the arrays of individuallycontrollable elements can have at least one of a common illuminationsystem (or part of an illumination system), a common support structurefor the arrays of individually controllable elements and a commonprojection system (or part of the projection system).

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors, such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein can be considered as synonymous with the moregeneral term “projection system”.

The projection system can image the pattern on the array of individuallycontrollable elements, such that the pattern is coherently formed on thesubstrate. Alternatively, the projection system can image secondarysources for which the elements of the array of individually controllableelements act as shutters. In this respect, the projection system cancomprise an array of focusing elements, such as a micro lens array(known as an MLA) or a Fresnel lens array, e.g., to form the secondarysources and to image spots onto the substrate. In such an arrangement,each of the focusing elements in the array of focusing elements can beassociated with one of the individually controllable elements in thearray of individually controllable elements. Alternatively, theprojection system can be configured such that radiation from a pluralityof the individually controllable elements in the array of individuallycontrollable elements is directed to one of the focusing elements in thearray of focusing elements and from there onto the substrate.

As herein depicted in the figures below, the apparatus is of areflective type (e.g., employing a reflective array of individuallycontrollable elements). Alternatively, the apparatus can be of atransmissive type (e.g., employing a transmissive array of individuallycontrollable elements).

The lithographic apparatus can be of a type having two (e.g., dualstage) or more (e.g., multiple stage) substrate tables. In such“multiple stage” machines the additional tables can be used in parallel,or preparatory steps can be carried out on one or more tables while oneor more other tables are being used for exposure.

The lithographic apparatus can also be of a type wherein at least aportion of the substrate can be covered by an “immersion liquid” havinga relatively high refractive index, e.g., water, so as to fill a spacebetween the projection system and the substrate. An immersion liquid canalso be applied to other spaces in the lithographic apparatus, forexample, between the contrast device and the projection system.Immersion techniques are well known in the art for increasing thenumerical aperture of projection systems. The term “immersion” as usedherein does not mean that a structure, such as a substrate, must besubmerged in liquid, but rather only means that liquid is locatedbetween the projection system and the substrate during exposure.

Although specific reference can be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein can haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin-film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein can be considered as within the scope of the more general terms“substrate” or “target portion,” respectively. The substrate referred toherein can be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein can be applied to such andother substrate processing tools. Further, the substrate can beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein can also refer to a substratethat already contains multiple processed layers.

Although specific reference can have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention can be used in otherapplications, for example imprint lithography, where the context allows,and is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device can be pressed into alayer of resist supplied to the substrate 114/214/314hereupon the resistis cured by applying electromagnetic radiation, heat, pressure or acombination thereof. The patterning device is moved out of the resistleaving a pattern in it after the resist is cured.

In another example, the invention can take the form of a computerprogram containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g., semiconductor memory, magnetic or optical disk) havingsuch a computer program stored therein.

Exemplary Environment

FIG. 1 schematically depicts a lithographic projection apparatus 100,according to one embodiment of the present invention. Apparatus 100includes at least a radiation system 102, an array of individuallycontrollable elements 104 (e.g., a contrast device or patterningdevice), an object table 106 (e.g., a substrate table), and a projectionsystem (“lens”) 108.

Radiation system 102 can be used for supplying a beam 110 of radiation(e.g., UV radiation, 248 nm, 193 nm, 157 nm, EUV radiation, e.g., 10-13nm, etc.), which in this particular case also comprises a radiationsource 112.

An array of individually controllable elements 104 (e.g., a programmablemirror array) can be used for applying a pattern to beam 110. Ingeneral, the position of the array of individually controllable elements104 can be fixed relative to projection system 108. However, in analternative arrangement, an array of individually controllable elements104 can be connected to a positioning device (not shown) for accuratelypositioning it with respect to projection system 108. As here depicted,individually controllable elements 104 are of a reflective type (e.g.,have a reflective array of individually controllable elements).

Object table 106 can be provided with a substrate holder (notspecifically shown) for holding a substrate 114 (e.g., a resist coatedsilicon wafer or glass substrate) and object table 106 can be connectedto a positioning device 116 for positioning substrate 114 with respectto projection system 108.

Projection system 108 (e.g., a quartz and/or CaF₂ lens system or acatadioptric system comprising lens elements made from such materials ora minor system) can be used for projecting the patterned beam receivedfrom a directing device 118 (e.g., a beam splitter).

Light is directed from directing device 118 onto a target portion 120(e.g., one or more dies) of substrate 114. Projection system 108 canproject an image of the array of individually controllable elements 104onto substrate 114.

The illumination 124 can comprise an adjusting device 128 for settingthe outer and/or inner radial extent (commonly referred to as (σ-outerand σ-inner, respectively) of the intensity distribution in beam 122. Inaddition, illuminator 124 will generally include various othercomponents. In this example, element 130 could be an integrator 130 andelement 132 could be a condenser 132, compared to the example discussedabove. In this way, beam 110 impinging on the array of individuallycontrollable elements 104 has a desired uniformity and intensitydistribution in its cross section.

It should be noted, with regard to FIG. 1, that source 112 can be withinthe housing of lithographic projection apparatus 100. In alternativeembodiments, source 112 can be remote from lithographic projectionapparatus 100. In this case, radiation beam 122 would be directed intoapparatus 100 (e.g., with the aid of suitable directing mirrors). It isto be appreciated that both of these scenarios are contemplated withinthe scope of the present invention.

Beam 110 subsequently intercepts the array of individually controllableelements 104 after being directed using directing device 118. Havingbeen reflected by the array of individually controllable elements 104,beam 110 passes through projection system 108, which focuses beam 110onto a target portion 120 of the substrate 114.

With the aid of positioning device 116 (and optionally interferometricmeasuring device 134 on a base plate 136 that receives interferometricbeams 138 via beam splitter 140), object table 106 can be moved, so asto position different target portions 120 in the path of beam 110. Whereused, the positioning device (not shown) for the array of individuallycontrollable elements 104 can be used to correct the position of thearray of individually controllable elements 104 with respect to the pathof beam 110, e.g., during a scan. In general, movement of object table106 is realized with the aid of a long-stroke module (coursepositioning) and a short-stroke module (fine positioning), which are notexplicitly depicted in FIG. 1. A similar system can also be used toposition the array of individually controllable elements 104. It will beappreciated that beam 110 can alternatively/additionally be moveable,while object table 106 and/or the array of individually controllableelements 104 can have a fixed position to provide the relative movement.

In an alternative configuration of the embodiment, substrate table 106can be fixed, with substrate 114 being moveable over substrate table106. Where this is done, substrate table 106 is provided with amultitude of openings on a flat uppermost surface, gas being fed throughthe openings to provide a gas cushion which is capable of supportingsubstrate 114. This is conventionally referred to as an air bearingarrangement. Substrate 114 is moved over substrate table 106 using oneor more actuators (not shown), which are capable of positioningsubstrate 114 with respect to the path of beam 110. Alternatively,substrate 114 can be moved over substrate table 106 by selectivelystarting and stopping the passage of gas through the openings.

Although lithography apparatus 100 according to the invention is hereindescribed as being for exposing a resist on a substrate, it will beappreciated that the invention is not limited to this use and apparatus100 can be used to project a patterned beam 110 for use in resistlesslithography.

The depicted apparatus 100 can be used in a plurality of modes:

1. Step mode: the entire pattern on the array of individuallycontrollable elements 104 is projected in one go (i.e., a single“flash”) onto a target portion 120. Substrate table 106 is then moved inthe x and/or y directions to a different position for a different targetportion 120 to be irradiated by patterned beam 110.

2. Scan mode: similar to step mode, except that a given target portion120 is not exposed in a single “flash.” Instead, the array ofindividually controllable elements 104 is movable in a given direction(the so-called “scan direction”, e.g., the y direction) with a speed v,so that patterned beam 110 is caused to scan over the array ofindividually controllable elements 104. Concurrently, substrate table106 is simultaneously moved in the same or opposite direction at a speedV=Mv, in which M is the magnification of projection system 108. In thismanner, a relatively large target portion 120 can be exposed, withouthaving to compromise on resolution.

3. Pulse mode: the array of individually controllable elements 104 iskept essentially stationary and the entire pattern is projected onto atarget portion 120 of substrate 114 using pulsed radiation system 102.Substrate table 106 is moved with an essentially constant speed suchthat patterned beam 110 is caused to scan a line across substrate 106.The pattern on the array of individually controllable elements 104 isupdated as between pulses of radiation system 102 and the pulses aretimed such that successive target portions 120 are exposed at thelocations on substrate 114. Consequently, patterned beam 110 can scanacross substrate 114 to expose the complete pattern for a strip ofsubstrate 114. The process is repeated until complete substrate 114 hasbeen exposed line by line.

4. Continuous scan mode: similar to pulse mode except that asubstantially constant radiation system 102 is used and the pattern onthe array of individually controllable elements 104 is updated aspatterned beam 110 scans across substrate 114 and exposes it.

In these first four exemplary modes, “partial coherent imaging” istypically performed for integrated circuit formation. Using thisimaging, each element in an array of individually controllable elementshas a unique tilt. The is positioned at the object plane and thesubstrate is positioned at the image plane of the imaging projectionoptics. Various illumination modes can be applied: annular,conventional, quadrupole, dipole etc. Also, different configurations foreach element in an array of individually controllable elements can beused to increase the “negative black” values: phase step mirrors,applying larger tilts, shaping the mirrors (butterfly, H-shape), or thelike.

Combinations and/or variations on the above described modes of use orentirely different modes of use can also be employed.

FIG. 2 depicts a lithographic apparatus 200, according to one embodimentof the present invention. For example, apparatus 200 can be especiallyuseful in the manufacture of flat panel displays using a pixel gridimaging mode, discussed below.

Projection system 208 can project images of secondary sources for whichthe elements of the array of individually controllable elements 204 actas shutters.

In an imaging grid array embodiment, projection system 208 can alsocomprise a micro lens array (MLA) to form the secondary sources and toproject microspots onto substrate 214.

Source 212 (e.g., a frequency tripled Nd:YAG laser in pixel grid imagingmode or an excimer laser in other modes) can produce a beam of radiation222. Beam 222 is fed into an illumination system (e.g., illuminator)224, either directly or after having traversed conditioning device 226,such as a beam expander, for example.

In one example, when apparatus 200 is operating in a pixel grid imagingmode, discussed below, illuminator 224 can comprise an adjusting devicefor setting a zoom to adjust a spot size of beam 222. In addition,illuminator 224 will generally include various other components, such asspot generator and a condenser. For example, spot generator can be, butis not limited to, a refractive or diffractive grating, segmentedmirrors arrays, waveguides, or the like. In this way, beam 210 impingingon the array of individually controllable elements 204 has a desiredzoom, spot size, uniformity, and intensity distribution in its crosssection.

As shown in FIG. 2, projection system 208 includes a beam expander,which comprises two lenses 250 and 252. First lens 250 is arranged toreceive a modulated radiation beam 210 and focus it through an aperturein an aperture stop 254. In one example, a lens 256 is located in theaperture. Radiation beam 210 then diverges and is focused by second lens252 (e.g., a field lens).

Projection system 208 further comprises an array of lenses 258 (e.g., amicrolens array (MLA)) arranged to receive expanded modulated radiation210. Different portions of the modulated radiation beam 210,corresponding to one or more of the individually controllable elementsin a patterning or contrast device 204, pass through respective lenses260 in MLA 258. Each lens 260 focuses the respective portion of themodulated radiation beam 210 to a point which lies on a substrate 214.In this way, an array of radiation spots 262 are exposed onto substrate214. Although only eight lenses 260 are shown, MLA 258 can comprise manythousands of lenses, which is also true of a number of individuallycontrollable elements in the array of individually controllable elementsused as patterning or contrast device 204.

The system in FIG. 2 allows for another mode of operation, Pixel GridImaging Mode. In this mode the pattern formed on substrate 214 isrealized by subsequent exposure of spots formed by spot generator 130that are directed onto array 204. The exposed spots have substantiallythe same shape. On substrate 214 the spots are printed in substantiallya grid. In one example, the spot size is larger than a pitch of aprinted pixel grid, but much smaller than the exposure spot grid. Byvarying intensity of the spots printed, a pattern is realized. Inbetween the exposure flashes the intensity distribution over the spotsis varied.

In one example, using this mode, which is typically used for formationof flat panel displays, individually controllable elements can begrouped into super-pixels. One super-pixel modulates the light of onespot at the substrate. The super-pixel is imaged at the entrance of anMLA in the exit pupil of each spot printed. The spot shape can beinfluenced by the illuminator through use of spot defining element(e.g., spot generators), zoom of blazing functions, or the like.

FIG. 3 illustrates schematically how a pattern on a substrate 314 isgenerated, according to one embodiment of the present invention. Forexample, this embodiment can be performed using the pixel grid imagingmode discussed above.

The darkened circles 362 represent spots recently projected ontosubstrate 314 by a MLA in a projection system, for example theprojection system as shown in FIG. 2. Substrate 314 is moved relative tothe projection system in a Y direction as a series of exposures areexposed on substrate 314.

The open circles 364 represent spots that have previously been exposedon substrate 314. As shown, each spot 362 projected onto substrate 314using the array of lenses within the projection system exposes a row 366of spot exposures 362/364 on substrate 314. The complete pattern forsubstrate 314 is generated by the sum of all the rows 366 of spotexposures 364 exposed by each of the spots 362. Such an arrangement iscommonly referred to as “pixel grid imaging,” which was discussed above.

It can be seen that the array of radiation spots 362 is arranged at anangle θ relative to substrate 314 (i.e., when the edges of the substrate314 lie parallel to the X and Y directions). This is done so that whensubstrate 314 is moved in a scanning direction (e.g., the Y-direction),each radiation spot 362 will pass over a different area of substrate314, thereby allowing the entire substrate to be covered by the array ofradiation spots. It will be appreciated that for ease of illustrationthe angle θ is exaggerated in FIG. 3.

It is to be appreciated that although 5×5 spots are shown in between twoneighboring spots of the MLA, in one example up to about 100×100 spotscan be used.

In one example, a spot grid at a substrate is about half a minimumlinewidth to be printed (e.g., from about 0.1 microns up to a fewmicrons), while a spot pitch at a MLA is about 100 micrometers up toabout a few hundred micrometers.

FIG. 4 shows schematically how an entire flat panel display substrate414 is exposed in a single scan through use of a plurality of opticalengines, according to one embodiment of the present invention. Eightarrays 468 of radiation spots are produced by eight optical engines (notshown), arranged in two rows 470,472 in a “chess board” configuration,such that the edge of one array of radiation spots slightly overlaps(e.g., in the scanning direction Y) with the edge of the adjacent arrayof radiation spots. In this example, a band of radiation extends acrossa width of substrate 414, allowing exposure of the entire substrate tobe performed in a single scan. It will be appreciated that any suitablenumber of optical engines can be used.

In one example, each optical engine can comprise a separate illuminationsystem, patterning device, and/or projection system, as described above.It is to be appreciated, however, that two or more optical engines canshare at least a part of one or more of the illumination system,patterning device, and projection system.

Each optical engine can comprise a separate illumination system,patterning device, and projection system, as described above. It is tobe appreciated, however, that two or more optical engines can share atleast a part of one or more of the illumination system, patterningdevice and projection system.

In order to manufacture a product using a lithographic process, a resistis uniformly applied to the surface of a substrate. A pattern ofradiation is then exposed on the resist such that some regions on theresist receive relatively high doses of radiation, while other regionsof the resist receive relatively low doses of radiation. The resistabove a given radiation dose threshold reacts and its stability ischanged. After the exposure process, the substrate is subjected tofurther processing operations, which remove the resist that has notreacted. Accordingly, the resist remains on the substrate in the regionsthat received a radiation dose above the given threshold, but is removedfrom the regions that received a radiation dose below the threshold,exposing the substrate. Accordingly, the resist remains on the substratein the regions receiving relatively high radiation doses and is removedfrom the regions on the substrate receiving a relatively low radiationdose. Therefore, by applying an appropriate pattern to the radiationbeam exposing the substrate, it is possible to generate a substrate witha pattern of regions of exposed substrate and regions covered by theresist. Subsequent processing steps are then performed to form part ofthe device on the substrate. For example, if a metal layer is applied tothe substrate before the resist, the metal layer that is not protectedby the patterned resist layer can be etched away. Accordingly, once theresist is removed, the substrate is left with a metal layer patternedaccording to the resist pattern, e.g., according to the pattern of theradiation beam.

It will be appreciated that a lithographic system is not limited to theexamples described above. For example, so-called ‘negative resists’ canbe used. When negative resist is used, radiation exposure of the resistmakes it less stable. Accordingly, it is the resist that receives aradiation dose above a given level that is removed in the post-exposureprocessing. Accordingly, the pattern of resist remaining on thesubstrate corresponds to the regions on the substrate that receives aradiation dose below a given threshold. Similarly, the pattern of resiston the substrate can be used for a variety of purposes. For example, theexposed regions of the substrate (i.e., those not protected by a layerof resist) can be subjected to processing steps such as ionimplantation.

The product pattern to be created on the substrate can be defined usinga vector design package, such as GDSII. In a maskless system, the outputfile from such a design package is processed in order to derive acontrol signal suitable for controlling the patterning device so that itreproduces a requested dose-map of radiation on the substrate asaccurately as possible. Where the patterning device comprises an arrayof individually controllable elements, the control signal containsinformation to manage switching of each element of the array ofindividually controllable elements for each flash of the radiation to bepatterned by the array (e.g., typical strobe frequencies being in theregion of 50 kHz for this application). Part of the processing can becarried out before exposure of the substrate begins (e.g., this is knownas off-line image processing) and/or part of the processing can becarried out simultaneously or during a short period of time (e.g., a fewseconds) immediately before the corresponding exposure (e.g., this isknown as in-line processing). Due to the enormous volume of data,in-line processing has to be managed carefully in order that the controlsignal can be provided at an acceptable speed and reasonable cost to thepatterning device.

FIG. 5 depicts a data-path 510 with data manipulation devices, accordingto one embodiment of the present invention. Data-path 510 notionallyincorporates all data processing and transmission components thattogether allow the requested dose-map (as defined by a user via an inputdevice 504) to be transferred to the patterning device 104/204 in anappropriate form. The data-path 510 comprises one or more datamanipulation devices, each configured to analyse an incoming data streamcomprising a (usually partly processed) version of the requesteddose-map and output the signal to the patterning device 104/204 or todevices that will process the data stream further before passing it onto the patterning device 104/204. For example, an “inverse-optics” datamanipulation device 512 (termed thus because it is concerned primarilywith the consequences of the optical arrangement of the projectionsystem) can be provided that is configured to calculate, for each pixelof the requested dose-map (which can for example be defined on a grid ofpoints relative to the substrate 114/214/314), the intensity fromcontributing pixels or groups of pixels in the patterning device 104/204in order to produce spot exposures SE with the appropriate dose. Theinverse-optics device 512 then forwards data towards the patterningdevice 104/204 in such a way that the requested dose-map can be built upover time as the array of radiation spots S moves over the surface ofthe substrate 114/214/314.

For each grid point on which the requested pattern is defined, theinverse-optics device 512 has to deal with spot exposure intensity datafor a number of spots 364 in the region of the grid point. Thisinformation is in turn derived from the requested pattern in the regionof the grid point. In general, a “context radius” can be defined aboutany given grid point in the requested pattern, which defines the regionof the requested pattern that has to be considered when calculating howto achieve the desired pattern at the grid point in question to aparticular accuracy. The size of the context radius will depend on theshape and positional deviation (from perfectly defined grid positions)of the point-spread function for the spot 364. It will typically bechosen to be several times the spot pitch and/or full width half maximum(FWHM) of the point spread function of each of the spots printed, whichmight therefore extend over several microns. Other data manipulationdevices, such as the “inverse-patterning-device” data manipulationdevice 514, will be described below.

In a typical application, the number of features to be written to thesubstrate 114/214/314 is enormous and data representing the wholerequested dose pattern will not be available at any one time to hardwarein the data-path 510 feeding the patterning device 104/204. As shown inFIG. 5, a rasterizer device 506 can be provided that converts thedescriptive representation of the desired pattern input by a user viadevice 504 into a sequence of data that substantially corresponds to asequence of spot 364 to be formed on the substrate 114/214/314 (notnecessarily the same sequence in which the spot 364 will actually beproduced—see below). Data representing the rasterized requested dosepattern is forwarded progressively over a period of time by therasterizer 506 over the data-path 510 (broken line portions in thedata-path represent sections which could comprise other datamanipulation devices dealing with other aspects of the patterningprocess) until all of the requested pattern has been written onto thesubstrate 114/214/314.

The requested dose-map can be expressed as a column vector comprisingelements that represent the dose at each one of a number of gridpositions defined on the substrate 114/214/314. The grid positions inthe requested dose-map can be specified relative to their coordinates inthe metrology frame coordinate system: x_(MF), y_(MF). As mentionedabove, this requested dose-map is to be built up from a collection ofspot 364. Each of these spot 364 will have a certain point-spreadfunction, which describes the cross-sectional spatial dependence oftheir intensity. In addition, there will be variations in the positionsof each of the spots from their expected positions in the spot grid dueto irregularities in the micro-lens array MLA used to focus the spots.Both the spot positions and the spot point-spread function shapes can beinput to the inverse-optics device 512 via a calibration data storagedevice 502.

The process of forming an image in this way is referred to as pixel gridimaging. Mathematically, the requested dose-map is set to be equal to asum over all possible spot 364 of intensity at each spot multiplied by apoint-spread function for each spot. This can be written as thefollowing equation:

${{D\left( {x_{MF},y_{MF}} \right)} = {\sum\limits_{n}^{{all}\mspace{14mu}{exposed}\mspace{14mu}{spots}}{I_{n} \cdot {{PSF}_{n}\left( {\left( {x_{MF} - x_{n}} \right),\left( {y_{MF} - y_{n}} \right)} \right)}}}},$

where I_(n) represents the individual spot exposure “intensity” for spotn (it is conventional to refer to an “intensity” but, as this isnormally proportional to energy dose, the parameter is sometimesexpressed in Joules), PSF_(n)((x_(MF)−x_(n)), (y_(MF)−y_(n))) representsthe point-spread function (the dose contribution at locationx_(MF)−x_(n) and y_(MF)−y_(n) of spot n), x_(n) and y_(n) indicate theposition of an individual exposed spot and D(x_(MF), y_(MF)) representsthe requested dose-map in the coordinates of the metroframe supportingthe lithographic apparatus.

The inverse-optics device 512 is configured to solve the following:given the requested dose-map and the point-spread function information(which is provided as calibration data), what are the individual spotexposure intensities (or corresponding desired sub-beam intensities)that need to be provided to image the requested dose-map as accuratelyas possible.

The above equation can be re-written in vector/matrix form as follows:[D]=[K]·[I],

where the column vector [D] represents the discrete (i.e., specified onspecific substrate grid positions only) requested dose-map, the columnvector [I] represents the individual spot exposure intensities and thematrix [K] represents the discrete point-spread functions.

Matrix [K] contains information on each individual spot exposurepoint-spread function (both position and shape). Therefore, according tothe present embodiment, the following information is used in order togenerate the matrix [K]: 1) scan speed/laser strobe frequency; 2)micro-lens array spot positions; 3) micro-lens array point spreadfunction shape (the spot point spread function of the whole opticalsystem, both projection/SLM and illumination); and 4) rotationalposition of the micro-lens array with respect the substrate scandirection (stage Y-axis).

In order to solve the above, the inverse-optics device 512 is arrangedto determine the individual exposed spot intensities such that[D]−[K]·[I] is minimized. In order to assess this minimum, anormalization is used. Due to the fact that this approach must beapplied in a pipeline environment (because not all of the spot exposureson the substrate are written at the same time) and the fact that one MLAspot is used to print many spot 364 (using many different laser pulses),it is to use the universal normalisation, in which specific knowledge ofthe requested pattern cannot be used. Use of such specific knowledgecould in principle be incorporated but would lead to a large increase inthe cost of the apparatus.

A least squares approach is therefore suitable and the to be solved bythe inverse-optics device 512 can therefore be expressed as:min_(I) _(n) ∥∥[D]−[K]·[I]∥ ₂.

Several approaches have been used for solving least squares s of thisgeneral type. These can be classed as follows: 1) Geometric, usingJacobians (this is an iterative approach), etc.; 2) Algebraic, using aniterative approach (e.g. Gauss-Seidel); and 3) Algebraic, using a directapproach (e.g. Gauss-Jordan, using a matrix inverse).

In one example, a method of the present embodiment falls into the thirdof these classes. It can be fast (once the inverse matrix has beendetermined) relative to options that require iteration, and allows theleast squares fit to be carried out effectively in real time. Inaddition, it displays deterministic behavior, which allows predictableconvergence and speed under a greater variety of conditions. Withiterative schemes, in contrast, it is often not possible to predict withgreat accuracy how long it will take for the solution to converge withinacceptable error limits. Furthermore, round offs due to limited wordsize in the data-path hardware are minimal for this approach due to theavoidance of re-use of intermediary results. Finally, there areimplementation benefits because the difficult preparation calculations(matrix inversion, etc.) can be performed offline in a large word sizedomain, e.g., a floating point domain, rather than having to carry outextra calculations during the actual imaging process (when the data pathis already processing a large volume of data).

One facet of the present embodiment is that the matrix [K] is notsquare. It has a size determined by the number of spot exposures n andthe number of discrete grid points at which the requested dose-map isspecified (the length of column vector [D]). Therefore, it may not bepossible to calculate the inverse of the matrix [K] using standardmathematical techniques. However, it is possible to proceed bycalculating a “pseudo-inverse” (see, e.g., “Linear Algebra and itsApplications,” Third Edition, Gilbert Strang, pages 449 and 450, whichis incorporated by reference in its entirety). In the description thatfollows, the pseudo-inverse is denoted as [K]⁺. The Moore-Penrosedefinition of the pseudo-inverse can be used, for example, but otheranalogous definitions can also be suitable.

The Moore-Penrose matrix inverse is a special case of a general type ofpseudo-inverse known as a “matrix 1-inverse”. It is sometimes referredto as the “generalized inverse”, or simply the “pseudoinverse”. TheMoore-Penrose inverse [K]⁺ of a matrix [K] satisfies the followingrelations (for real valued matrices):[K][K]⁺[K]=[K],[K]⁺[K][K]⁺=[K]⁺,([K][K] ⁺)^(T) =[K][K] ⁺, and([K] ⁺ [K])^(T) =[K] ⁺ [K].

The shortest least squares solution to the [D]=[K]·[I] (which wasexpressed as min_(I) _(n) ∥[D]−[K]·[I]∥₂, see above) can be written inthe following form: [I]=[K]⁺·[D].

If the inverse of ([K]^(T)[K]) exists, then the pseudo-inverse [K]⁺ canbe expressed as:[K] ⁺=([K] ^(T) [K])⁻¹ [K] ^(T),

where [K]^(T) is the matrix transpose. This can be seen bypre-multiplying both sides of the equation [D]=[K]·[I] by [K]^(T) tocreate a square matrix ([K]^(T) [K]), which can be inverted normally,giving:[I]=([K] ^(T) [K])⁻¹ [K] ^(T) ·[D]≡[K] ⁺ ·[D].

Avoiding negative intensity solutions in the direct algebraicleast-squares fit, sub-spot-exposure-grid position dependence andpattern angular dependence

The requested dose map (which can equal to the rasterized Flat PanelDisplay pattern, for example) is frequently designed to produce sharplydefined resist features. The corresponding dose patterns are built upfrom spot 364 (which can be Gaussian shaped, for example) and fittingroutines (such as the least-squares fit discussed above) will generallyyield solutions with negative intensity components (i.e., spot 364 thatwould tend to cause a reduction in dose at points on the substrate114/214/314 on which they fall). Unfortunately, negative contributionsmay not be possible in systems where neighboring spot 364 are formedincoherently (e.g., because they arrive at different times) because theassociated sub-beams of radiation cannot interfere destructively witheach other. The dose at a given point on the substrate 114/214/314 isthen built up from a sum of intensities from different sub-beams ratherthan a sum of amplitudes.

The negative intensity components can be neglected (set to zero, forexample) but this leads to a fit that reproduces the requested dosepattern only to a limited accuracy.

A related issue is that of unwanted position dependence in the patternformed on the substrate 114/214/314. In particular, there is a tendencyfor the requested dose pattern to be more perfectly attained near togrid positions in the array of spot 364. One reason why this occurs isthat errors linked to the inability to produce negative intensity areless pronounced in these regions relative to points in between the gridpositions (see below). As a result of this, dense features printed at aperiod close to the grid period will suffer from a low frequency (thedifference frequency between the period of the feature and the period ofthe grid) feature shape variation (“beating”).

One of the effects of this sub-spot-exposure-grid position dependence isthat device features will be formed differently depending on theirposition and/or orientation relative to the grid. For example, featureswith edges parallel to the grid can be formed particularly well (if theedge lies along the grid positions themselves) or particularly badly (ifthe edge lies exactly between rows of the grid). Features with edges atintermediate angles can be microscopically jagged.

Also, the grid of radiation spots can have a translational or rotationaleffect on the resulting pattern (especially an image log slope variationas a function of the position and angle with respect to the grid ofradiation spots).

According to one or more embodiments of the present invention, theseissues can be at least partially overcome by applying a low pass filter508 (a two dimensional filter, for example) to the requested dosepattern data (or derivative thereof) to form a frequency-clipped targetdose pattern that is fed into the inverse-optics device 512.Alternatively, the filter can be incorporated into the point-spreadfunction matrix [K] to equivalent effect.

A low-pass filter can include any filter that completely or partiallyremoves frequency components from a signal above a selected thresholdfrequency. The frequency cutoff can be sudden/sharp or gradual and theshape of the cutoff can be adjusted so as better to match theamplitude-frequency response of the requested dose map to theamplitude-frequency response of the spot exposures and/or patterningdevice, for example. More generally, the filter can be designedspecifically to match the amplitude-frequency response of the requesteddose map to the amplitude-frequency response of spot 364 and/or thepatterning device.

The development and application of the filter can be described startingfrom the equation:

${D\left( {x_{MF},y_{MF}} \right)} = {\sum\limits_{n}^{{all}\mspace{14mu}{exposed}\mspace{14mu}{spots}}{I_{n} \cdot {{PSF}_{n}\left( {\left( {x_{MF} - x_{n}} \right),\left( {y_{MF} - y_{n}} \right)} \right)}}}$

and transforming it into the Fourier domain. In one example, the pointspread function for each of the spot 364 is a two-dimensional Gaussian(an alternative example would be an airy disc; the invention is notlimited to any particular shape of spot exposure 364), defined as:

${{PSF}_{n}\left( {\left( {x_{MF} - x_{n}} \right),\left( {y_{MF} - y_{n}} \right)} \right)} = {\frac{1}{2{\pi \cdot \sigma^{2}}}{\exp\left( \frac{{- \left( {x_{MLA} - x_{n}} \right)^{2}} + \left( {y_{MLA} - y_{n}} \right)^{2}}{2 \cdot \sigma^{2}} \right)}}$

or, rewritten in terms of the full-width-half-maximum d_(fwhm):

${{PSF}_{n}\left( {\left( {x_{MF} - x_{n}} \right),\left( {y_{MF} - y_{n}} \right)} \right)} = {\frac{4 \cdot 2 \cdot {\ln(2)}}{2{\pi \cdot d_{fwhm}^{2}}}{\exp\left( \frac{{- 4} \cdot 2 \cdot {\ln(2)} \cdot \left( {\left( {x_{MLA} - x_{n}} \right)^{2} + \left( {y_{MLA} - y_{n}} \right)^{2}} \right)}{2 \cdot d_{fwhm}^{2}} \right)}}$

The Fourier transform of

${{D\left( {x_{MF},y_{MF}} \right)} = {\sum\limits_{n}^{{all}\mspace{14mu}{exposed}\mspace{14mu}{spots}}{I_{n} \cdot {{PSF}_{n}\left( {\left( {x_{MF} - x_{n}} \right),\left( {y_{MF} - y_{n}} \right)} \right)}}}},$

under the above assumption is:

${\overset{\sim}{D} = {\sum\limits_{n}^{{all}\mspace{14mu}{exposed}\mspace{14mu}{spots}}{I_{n} \cdot {\exp\left( {{{- j}\; x_{n}k_{x}} - {j\; y_{n}k_{y}}} \right)} \cdot {\exp\left( \frac{{- \left( {k_{x}^{2} + k_{y}^{2}} \right)} \cdot d_{fwhm}^{2}}{16 \cdot {\ln(2)}} \right)}}}},$

where k_(x) and k_(y) are the two-dimensional angular spatialfrequencies and {tilde over (D)} is the Fourier transform ofD(x_(MF),y_(MF)).

This last equation shows that the pattern position information isrepresented in the phase of {tilde over (D)} and the shape informationin the amplitude.

The spatial filter F is applied as {tilde over (F)}·{tilde over (D)}(i.e., a multiplication in the Fourier domain). The operation can alsobe viewed as a convolution between a corresponding non-Fouriertransformed filter F and D(x_(MF),y_(MF)).

The filter should not influence the pattern position information.Therefore, the filter should be chosen to have a linear phase behavior.For example, symmetrical FIR (Finite Impulse Response) filters (for thepurposes of this application, a convolution with a symmetrical shape isconsidered to fall within this class), which have a suitable linearphase behavior, can be used. Any resulting phase effect of such filterscan be made zero by applying an additional translation.

The filter should not normally affect the size/dose of the patternshapes, so the DC filter gain is normally chosen to be 1.

As discussed above, one of the issues with the amplitude-frequencyresponse of the spot 364 is that it is not possible to create negativelight (i.e. negative amplitudes) with incoherent imaging (although thisis possible with coherent imaging). A further issue is that thefrequency response of the spot 364 varies according to the position ofthe pattern with respect to individual spot exposure grid positions(i.e., this is one cause of the sub-exposure-grid position dependencementioned above). This means that a filter designed to work for dosepattern elements in one part of the sub-exposure-grid may not work aseffectively for dose pattern elements defined at other positions in thesub-exposure-grid.

The extent to which sub-exposure-grid position dependence is an issuewill, in general, depend on the nature of the spot exposure grid. Therectilinear nature of device elements, for example, means thatsquare/rectangular spot exposure grids (where a unit cell with square orrectangular symmetry can be identified) are more likely to suffer due tothe increased likelihood of device elements or edges lying along “worstcase” lines in the exposure grid (see below for what is meant by “worstcase”). In such a scenario, it is desirable to configure the filter 508to cope with “worst case” points in the sub-exposure-grid. On the otherhand, the effect of sub-exposure-grid variation on device structures inother exposure grid geometries (such as hexagonal or quasi-hexagonal,for example) can tend to average out so that a lighter filter can beused, configured to cope merely with an average rather than a “worstcase” position. By quasi-hexagonal geometry, what is meant is anarrangement derivable by a simple scaling along x and/or y from purehexagonal geometry (pure hexagonal geometry being defined as a gridgeometry that can be built up from unit cells with hexagonalsymmetry—similar to a 2D “close-packed” structure). In general, theappropriate strength of the filter 508 will depend on the particularspot exposure grid geometry.

According to one example, a filter 508 is developed based on the Fouriertransform of the spot exposure grid impulse response (this refers to theresponse of the spot exposure grid to a requested dose patternconsisting of a Dirac delta-function at a particular point). In general,one or more spots will be used to image the impulse, the numberdepending on the sub-exposure-grid position and exposure grid geometry,as discussed further below.

FIG. 6 depicts a portion of a square spot exposure grid and a “worstcase” position, according to one embodiment of the present invention.FIG. 7 depicts a portion of a hexagonal spot exposure grid and a “worstcase” position, according to one embodiment of the present invention.Thus, FIGS. 6 and 7 show example grid geometries (rectangular andhexagonal respectively). For a rectangular grid, at most four spotexposures are used to expose an impulse response. For a hexagonal grid,at most three spot exposures are used to expose an impulse response. Ineach case, the actual number will depend on the sub grid position atwhich the impulse response is requested.

The generalized Fourier transform of the impulse response for a grid(assuming a Gaussian spot shape) is

${\overset{\sim}{H} = {\sum\limits_{n}^{{all}\mspace{14mu}{exposed}\mspace{14mu}{spots}}{I_{n} \cdot {\exp\left( {{{- j}\; x_{n}k_{x}} - {j\; y_{n}k_{y}}} \right)} \cdot {\exp\left( \frac{{- \left( {k_{x}^{2} + k_{y}^{2}} \right)} \cdot d_{fwhm}^{2}}{16 \cdot {\ln(2)}} \right)}}}},$

where k_(x) and k_(y) are the two-dimensional angular spatialfrequencies, d_(fwhm) indicates the full width half maximum of the spot364, I_(n) indicates the spot exposure intensity of spot n, and x_(n)and y_(n) indicate the spot exposure position of spot n.

If an impulse response is requested exactly on a grid position, it is toactivate one spot exposure 364 in order to expose it. This is referredto as a “best case.” The Fourier transform of this best case impulseresponse of a spot exposure grid is:

${\overset{\sim}{H}}_{{best}\mspace{14mu}{case}} = {\exp\left( \frac{{- \left( {k_{x} + k_{y}} \right)} \cdot d_{fwhm}^{2}}{16 \cdot {\ln(2)}} \right)}$

A so-called worst case situation arises for a requested impulse exactlyhalf-way between two exposed spots (both hexagonal and rectangular).Examples of these positions (indicated by “−”) are given in FIGS. 6 and7. The 1-dimensional Fourier transform of this worst case impulseresponse (taken along the worst case trajectory, x_(n)=0) is as follows:

${\overset{\sim}{H}}_{{worst}\mspace{14mu}{case}} = {\frac{1}{2} \cdot {\exp\left( {{{{- j} \cdot 0.5 \cdot k_{y}}p} + {{j \cdot 0.5 \cdot k_{y}}p}} \right)} \cdot {\exp\left( \frac{{- \left( {k_{x}^{2} + k_{y}^{2}} \right)} \cdot d_{fwhm}^{2}}{16 \cdot {\ln(2)}} \right)}}$

where p indicates the spot exposure grid pitch.

FIG. 8 depicts a portion of a square spot exposure grid with “worstcase” lines and “best case” positions, according to one embodiment ofthe present invention. FIG. 9 depicts a portion of a hexagonal spotexposure grid with “worst case” positions and “best case” positions,according to one embodiment of the present invention. FIGS. 8 and 9 showhow worst case (“−”) and best case (“+”) positions are distributed inthe rectangular and hexagonal grid geometries, respectively. As can beseen, in the case of the hexagonal spot exposure grid, discrete pointsexhibit the worst case impulse response behavior under specific angles.In the case of the rectangular spot exposure grid, worst case points liealong continuous lines covering the entire substrate. These lines lie atspecific, but very common device feature angles. It can be seen that, ina rectangular grid, the number of positions (statistically) of the worstcase impulse response far exceeds the number of similar positions in thehexagonal spot exposure grid. Therefore, the average performance of thehexagonal grid from this point of view is likely to be better than thatof the rectangular spot exposure grid. This improvement is relevant forthe system behavior, which is determined by, amongst other things, thelow-pass fit filter 508 described above.

An exemplary discussion of best and worst case scenarios for rectangularand hexagonal spot exposure grids can be found in U.S. Ser. No.11/018,929, filed Dec. 22, 2004, which is incorporated by referenceherein in its entirety.

The low pass fit filter 508 can be applied for various reasons, forexample, (1) to avoid the need for negative light; (2) to minimize theinfluence of the sub-spot-exposure-grid position; and (3) to minimizethe influence of the angle between an image feature and the spotexposure grid on the resulting aerial image. It is found that for ahexagonal spot exposure grid, higher spatial frequencies can be allowedto enter the fitting algorithm of the inverse-optics device 512 withoutincreasing the maximum negative solution with respect to the case inwhich a rectangular spot exposure grid is used.

In one example, the filter 508 is configured to operate in a circularlysymmetric manner (with respect to radial axes lying in the plane of thesubstrate) and matches the worst-case spot exposure grid impulseresponse. The extent to which it is used to allow for the worst-caseimpulse response can depend on the shape of the grid. In grids whereworst case points lie at discrete grid positions (rather than alonglines), it can be sufficient for a weaker filter to be used. Withdifferent shaped grids it can be more effective to choose anintermediate position (relative to the worst and best case positions),particularly where the worst case points line at discrete positions(rather than along lines).

The filter 508, according to this example, is also designed so assimultaneously to maximize the performance of the pixel grid imaging interms of the CD, CDU and dose uniformity (by removing just enough of thehigher frequencies to solve the abovementioned problems and, ideally, nomore).

Rectangular Spot Exposure Grid Filter

As mentioned above, the 1-dimensional Fourier transform of the worstcase impulse response can be written as:

${\overset{\sim}{H}}_{{worst}\mspace{14mu}{case}} = {\frac{1}{2} \cdot {\exp\left( {{{{- j} \cdot 0.5 \cdot k_{y}}p} + {{j \cdot 0.5 \cdot k_{y}}p}} \right)} \cdot {\exp\left( \frac{{- \left( {k_{x}^{2} + k_{y}^{2}} \right)} \cdot d_{fwhm}^{2}}{16 \cdot {\ln(2)}} \right)}}$

where p indicates the spot exposure grid pitch. The magnitude of thisworst case impulse response described by the above equation becomesnegative at k_(y)=π/2 so that a filter with low-pass properties, such asto suppress spatial frequencies greater than this value will avoidnegative amplitudes. If the filter 508 is strong enough to cope with theworst case grid points, then it will also be sufficient to avoidnegative amplitudes for other positions in the sub exposure grid. Usinga stronger filter 508 (e.g., with a cut-off at an even lower frequency)will unnecessarily degrade the performance of the spot exposure grid andlead to a dose pattern of reduced resolution.

Following on from the above discussion, a suitable filter can be atwo-dimensional circularly symmetrical FIR filter, based on thefollowing one-dimensional truncation:

${\overset{\sim}{F}}_{{{fit}\mspace{14mu}{filter}};{rect}} = \left\{ \begin{matrix}{{{\overset{\sim}{H}}_{worstcase}\left( {{k_{x} = 0},\mspace{14mu}{k_{y} = \omega}} \right)}} & {{{when}\mspace{14mu}\omega} < \frac{\pi}{p}} \\0 & {{{when}\mspace{14mu}\omega} \geq \frac{\pi}{p}}\end{matrix} \right.$

where ω=π/p is the one-dimensional angular spatial frequencycorresponding to the spot exposure grid pitch.

Hexagonal Spot Exposure Grid Filter

FIG. 10 depicts the hexagonal spot exposure grid geometry and shows an“intermediate case” position, according to one embodiment of the presentinvention. The filter for this geometry of exposure grid can bedeveloped starting from the Fourier transformed impulse response for aposition exactly in between three spots. The position shown in FIG. 10represents the intermediate position between the worst and best cases(see FIG. 9). The Fourier transformed impulse response of the centralposition shown is:

${\overset{\sim}{H}}_{{central};{hex}} = {\frac{1}{3} \cdot \left\{ {{\exp\left( {{- j}{\frac{1}{\sqrt{3}} \cdot p \cdot k_{x}}} \right)} + {\exp\left( {{j{\frac{\sqrt{3}}{6} \cdot p \cdot k_{x}}} - {j \cdot \frac{1}{2} \cdot p \cdot k_{y}}} \right)} + {\exp\left( {{j{\frac{\sqrt{3}}{6} \cdot p \cdot k_{x}}} + {j \cdot \frac{1}{2} \cdot p \cdot k_{y}}} \right)}} \right\} \cdot {\exp\left( \frac{{- \left( {k_{x}^{2} + k_{y}^{2}} \right)} \cdot d_{fwhm}^{2}}{16 \cdot {\ln(2)}} \right)}}$

where p indicates the spot exposure grid pitch.

A suitable filter in this case can be a two-dimensional circularlysymmetrical FIR filter, based on the following one-dimensionaltruncation:

${\overset{\sim}{F}}_{{{fit}\mspace{14mu}{filter}};{hex}} = \left\{ \begin{matrix}{{{\overset{\sim}{H}}_{worstcase}\left( {{k_{x} = 0},\mspace{14mu}{k_{y} = \omega}} \right)}} & {{{when}\mspace{14mu}\omega} < \frac{4\pi}{3p}} \\0 & {{{when}\mspace{14mu}\omega} \geq \frac{4\pi}{3p}}\end{matrix} \right.$

where ω=4π/3p is the one-dimensional angular spatial frequencycorresponding to 0.75 times the spot exposure grid pitch.

For both the rectangular and hexagonal spot exposure grid filters 508discussed above, the fitted solution provided by the inverse-opticsdevice 512 does not use large negative exposed spot intensities in orderto image the requested dose map to a high level of precision. In fact, atypical solution will contain only very small negative exposed spotintensities, which can be clipped to zero. In one example, small “stray”positive values, arising as a side effect from the filtering process,can also be clipped to zero—these can otherwise lead to small butsignificant amounts of “stray light” in areas far away from the edges ofpattern features. The effect of this clipping results in some very faintdose intensity in small parts of a region neighboring an image featurewhere no light has been requested. These positions are typically locatedwithin a band of around 1.5 microns from the actual edge, so that theinfluence on the device to be formed can normally be neglected.

In general, the low pass filter could be arranged to operate eitherpartially or completely in an offline part of the data-path, afterrasterization, or as a part of the rasterization process. In addition,although the above embodiments refer to a direct algebraic least-squaresfit of the spot exposure intensities to the frequency-clipped targetdose pattern, it would also be possible to adapt the use of the low-passfilter to the case where an indirect/iterative approach is used.

An Image Sharpening Filter

FIG. 11 depicts a low-pass 1102 and sharpening filter 1104, according toone embodiment of the present invention. FIG. 11 shows an alternativeembodiment of the invention in which the filter 508 has a split or dualfunctionality, comprising a low pass filter part 1102 and a sharpeningfilter part 1104. The sharpening filter 1104 can be used to improve thedefinition of features in the dose pattern, making use of the knowledgeof the product features to be formed. In general, the sharpening filter1104 will comprise a contribution corresponding to the inverse of theimage feature to be sharpened (in the Fourier domain). Taking as anexample the smallest possible circular product feature (with a diameterequal to the critical dimension CD), the sharpening filter function canbe defined as follows in the spatial domain:

$H = \left\{ \begin{matrix}\frac{1}{\pi \cdot R_{sharp}^{2}} & {{{when}\mspace{14mu}\sqrt{x^{2} + y^{2}}} \leq R_{sharp}} \\0 & {{{when}\mspace{14mu}\sqrt{x^{2} + y^{2}}} > R_{sharp}}\end{matrix} \right.$

where R_(sharp) is the radius of the image feature (here, half the CD).Transforming the image feature into the Fourier domain yields

$\overset{\sim}{H} = {2 \cdot \frac{J_{1} \cdot \left( {R_{sharp} \cdot \sqrt{k_{x}^{2} + k_{y}^{2}}} \right)}{R_{sharp} \cdot \sqrt{k_{x}^{2} + k_{y}^{2}}}}$

where J₁ is a Bessel function of the first kind.

The sharpening filter 1104 corresponding to this example is then theinverse of the amplitude frequency response of the Fourier transform ofthe smallest possible circular symmetrical image feature:

${\overset{\sim}{F}}_{{sharp}\mspace{14mu}{filter}} = \left\{ \begin{matrix}{\frac{\omega \cdot R_{sharp}}{2 \cdot {J_{1}\left( {\omega \cdot R_{sharp}} \right)}}} & {{{when}\mspace{14mu}\omega} \leq \frac{\pi}{p}} \\{{\overset{\sim}{F}}_{{sharp}\mspace{14mu}{filter}}\left( {\omega = \frac{\pi}{p}} \right)} & {{{when}\mspace{14mu}\omega} > \frac{\pi}{p}}\end{matrix} \right.$A Filter for Controlling the Image Log Slope

FIG. 12 depicts an image log slope filter, according to one embodimentof the present invention. The “image log slope” refers to the spatialdependence of the dose pattern written to the substrate and inparticular to the rate of change (or slope) of dose with distance dI/dx.It can be useful for a user of the lithography machine to be able toadjust this slope for several reasons. Firstly, a shallower image logslope means that features formed after substrate processing will tend tohave more rounded edges, which can reduce the risk of electrostaticdischarge (sparks). Secondly, a shallower slope can make it easier toachieve satisfactory overlap between features on different processlayers on the substrate. Overlap generally has to be controlled withgreater precision where features themselves are sharply defined in anyone process layer (i.e., having a steep image log slope). Thirdly, inflat panel displays produced by lithography, for example, the viewingangle is dependent on the image log slope of individual features. Ashallower image log slope can lead to a larger viewing angle (perhaps atthe expense of resolution, contrast ratio, etc.), which can be desirablefor certain applications (e.g., in television or video).

The filter 508 can comprise an image log slope filter 1202 for thispurpose. It is not generally possible in this way to adjust the contrastabove the maximal contrast determined by the worst case spot exposureimpulse response, so the filter will normally act to reduce thecontrast.

An example image log slope filter function in the spatial domain is:

$F_{slope} = \left\{ \begin{matrix}\frac{1}{\pi \cdot R_{slope}^{2}} & {{{when}\mspace{14mu}\sqrt{x^{2} + y^{2}}} \leq R_{slope}} \\0 & {{{when}\mspace{14mu}\sqrt{x^{2} + y^{2}}} > R_{slope}}\end{matrix} \right.$

The filter function is determined such that the DC gain of the filteris 1. The radius R_(slope) is the parameter that influences the imagelog slope.

Alternatives to Filters

In one example, as an alternative to manipulating the control signal tobe sent to the patterning device 104/204 using filters, it can also bepossible to modify the illumination and projection optics in order tochange the spot shape. Different spot shapes can be realized by beamshaping and stops. Spot shapes realized can be, for example: a Gaussianbeam (in case of multiple laser beam propagation), an airy disk (by atruncating aperture), a circular tophead light distribution or aconvolution of any of the above.

In one example, filters can provide a cheaper and more easily adaptablesolution because they do not require major additions of new types ofhardware. Instead, an increase in the capacity of existing hardwareand/or reconfiguration can be sufficient.

Combining Filters

In one example, it is possible to produce a combined filter thatperforms the functions of two or more of the filters discussed above. Inthe case where the combined filter is formed from the low pass filter1102, sharpening filter 1104 and image log slope filter 1202, thecombined filter in the spatial domain is formed by a convolution asfollows:F_(combined filter)=F_(fit filter)

F_(sharp)

F_(slope)

where

represents “convoluted with” (both here and throughout thespecification). As the convolution operation satisfies the property f

g=g

f, the order in which the filters are combined does not make anydifference.

In one example, the filters thus defined (combined with each other orotherwise) can also be combined with the pseudo-inverse matrix [K]⁺(instead of using a separate filter step that filters the requested dose[D]) as follows:[I]=F _(combined filter)

[K] ⁺ ·[D],which results in[I]=[K] ⁺ _(filtered) ·[D].

Filtering the kernel [K]⁺ and not the requested dose [D] can have thefollowing attributes: a) the dynamic range of the kernel is reduced(kernel values are smeared out), which reduces the word size; and b) thecontext radius is reduced (for a similar imaging performance)substantially.

In one example, the filtered kernel [K]⁺ _(filtered) can be preparedcompletely off-line. At least, this is true to the extent that: the MLAspot positions do not vary during a single substrate exposure; the MLApoint-spread function shape does not vary; the MLA position variationcan be compensated in the data-path; and the scan speed and laserfrequency are constant.

Filters for Applying CD Biasing

In one example, critical dimension biasing (CD biasing) is used. CDbiasing is concerned with the step of adjusting the minimum line widthaccording to customer needs. This step is frequently used because, whilethe line width of the dose pattern can be predictable to a high degree,the actual line width of the feature formed after processing is lesspredictable and can benefit from adjustment in order to achieve optimalperformance. This adjustment can be implemented by biasing the CD (i.e.,increasing the CD to form thicker lines or decreasing the CD to formthinner lines).

In mask-based lithographic systems, CD biasing is normally achieved bychanging the overall intensity of the radiation source. An increasedintensity for each sub-beam of radiation tends to spread out the doseassociated with individual pattern features, which leads to a changed CD(CD increase is applicable to clear aerial images, CD decrease isapplicable to dark aerial images-bright field)). This and similarapproaches have the drawback that a change in CD induced along one axisparallel to the substrate can be accompanied by a corresponding changein CD along the orthogonal axis. This limitation is not a problem if thecustomer requires equal adjustment along both the X and Y axes, but ahigher level of optimization would generally be possible if the CD couldbe adjusted independently for each axis (e.g., change the CD along X,but not Y). More importantly, it would be preferable to adjust sizes anddensities on a feature-by-feature basis, for a sub-set of, or for all,feature types (e.g., dense, isolated, lines, contacts etc.).

FIG. 13 depicts a CD biasing filter 1302, according to one embodiment ofthe present invention. Independent X and Y CD biasing is performed byproviding CD basing filter 1302 to manipulate the control signal sent tothe patterning device 104/204, rather than the illumination dose, tochange the CD. This method can also be used to provide a CD that varieswith position (and, possibly, independently in X and Y) over thesubstrate 114/214/314. This can be achieved through the use of a CDbiasing filter 1302 in an analogous way to the filters discussed above.In particular, the CD biasing filter 1302 can be used to modify therequested dose map data to be input to the data manipulation device 500(two such devices are shown for illustrative purposes). This filteringoperation would normally be arranged to be carried out off-line as itcan be difficult to implement such functionality in the fittingalgorithm itself (as performed by the inverse-optics device 512). Inthis example, the CD biasing filter 1302 is positioned before therasterizer 506. In one example, if inline control is used, this canstill be achieved (as in mask-based systems), possibly in combinationwith the offline method discussed above, by varying the intensity of theradiation source, for example, or using a dilation/erosion algorithm(see above).

Alternatively or additionally, CD biasing can be applied using themathematical morphology operations known as dilation and erosion. Thedilution operation can be applied to a mathematically defined object tocause it to dilate, or grow in size, while erosion causes objects toshrink. The amount and manner in which the objects are caused to grow orshrink is specified by a so-called structuring element. This method canbe applied digitally either inline or offline.

On-The-Fly Focus Correction

Focus correction can be achieved by varying the position of thesubstrate table WT 106/206, in response to measurements of the bestfocus position, as the substrate table WT 106/206 is moved relative tothe substrate 114/214/314. In principle, all or part of the projectionsystem 108/208 can also be moved to achieve the same effect. In eithercase, both translation and rotational (tilt) displacements can be used.

Systems such as these are expensive in terms of servos and the extracontrol systems that are used for an efficient implementation. Inaddition, the spatial resolution of the focus correction is limited atbest by the size of the spot grid associated with a given MLA andoptical column. Sub-sections of the optical column and/or substratetable 106/206 cannot normally be moved independently with respect toeach other and the substrate 114/214/314. In addition, there is a limitto how quickly such systems can respond to changes in the best focusposition due to the inertia of the component that is to be displaced.

In one example, best focus is performed via a data-path (i.e., bymanipulating the control signal to be fed to the patterning device104/204). This is possible because the focus influences the full widthhalf maximum of the point spread functions for each spot exposure 364.Calculations based on measurements of the true focus position relativeto particular points on the substrate 114/214/314 can be input ascalibration data into the point spread function matrix [K]. The controlsignal sent to the patterning device 104/204 can thus be adapted to takeaccount of out-of-focus regions on the substrate 114/214/314 where thespot exposure shape will be slightly wider than normal. The result ofsuch spot correction is that focus can effectively be achieved to ahigher degree. This is due partly to the increased spatial resolution(limited by the size of individual spot exposures rather than the sizeof the whole spot grid) and partly by the quicker response time (noextra mechanical movement is performed). This can be achieved withoutadding any major new hardware (such as servo/control systems), althoughadditional computational hardware can be used to add the extra capacityin the data-path 510. In one example, focus control in this way canallow a mechanical focus control apparatus to be removed or simplified,thus reducing costs and/or space. Alternatively, a high resolutionsystem can be devised using a combination of mechanical focus control(as a “coarse” adjustment) and data-path focus correction (as a “fine”control). Coarse and fine adjustment can refer to predominantly lowspatial frequency and predominantly high spatial frequency correctionrespectively.

In one example, the correction applied by the data-path can take intoaccount effects that remain constant from scan to scan, for examplefocus variations from lens to lens in the MLA. In this scenario, thecorrection can be implemented via offline calculations and an offlineadjustment to the point spread function matrix [K] to be used by theinverse-optics data manipulation device 512. However, the correction canalso be applied in-line to provide an “on-the-fly” correction foreffects that can vary from scan to scan, such as those associated withimperfections in the substrate topology or in the substrate tabletransport.

FIG. 14 depicts an apparatus suitable for on-the-fly focus correctionvia a data-path, according to one embodiment of the present invention.This embodiment can also use coarse and fine control discussed above.Focus data is obtained by analyzing radiation from a radiation source1410, which is received, after reflection from various positions on thesubstrate 114/214/314 and/or substrate table 106/206, by a radiationdetector 1408. This analysis can be carried out by a focus controldevice 1402. Alternatively, the position of the substrate table 106/206and substrate 114/214/314 can be determined at various points bymeasuring the travel times of ultrasonic waves emitted by one or moreultrasonic transducers rigidly attached to the projection system 108/208after reflections from the substrate 114/214/314 and/or substrate table106/206.

Based on the focus data thus obtained, the focus control device 1402calculates a best focus position for a portion of the substrate114/214/314 and outputs a control signal along either or both of datapathways 1412 and 1414 to either or both of a projection system positionand/or tilt controller 1404 and a substrate table position and/or tiltcontroller 1406. The projection system position and/or tilt controller1404 and/or substrate table position and/or tilt controller 1406 arethus caused to perform translation and/or tilt operations of theprojection system 108/208 and/or substrate table WT 106/206 in order tobring the region at the substrate 114/214/314 to be exposed into aposition closer to the best focus plane. According to this embodiment,this is the so-called “coarse” control.

Fine control is achieved via the data-path 510. The focus control device1402, after forwarding the control signal to the controllers 1404 and1406, is configured also to forward focus data to a data-path focuscontrol device 1416, which calculates the adjustments that need to bemade to the matrix [K] in order to take account of changes in the pointspread function performance that should be expected due to variations inthe quality of the focus.

In one example, the combination of coarse and fine correction can beimplemented in the following sequence: measure focus; carry out coarsecorrection; re-measure focus; carry out fine correction. In thissequence, the focus data sent to the coarse device will be differentfrom that sent to the fine correction device each time (assuming somefocus error is always detected). Alternatively, the coarse and finecorrection can be carried out simultaneously. In this case, the datasent to the data-path focus control device 1416 includes the controlsignal sent to the controllers 1404 and 1406. The correction to thematrix [K] will then take account of the expected movement(s) of thesubstrate table 106/206 and/or projection system 108/208. Therelationship between values of a control signal sent to one or both ofcontrollers 1404 and 1406 and the resultant changes in focus can berecorded in a calibration table.

In the embodiment shown, the focus correction data is passed to thedata-path via the storage device 502 which provides the spot positionand spot point spread function information (which can be updated by thefocus correction data) to the inverse optics data manipulation device512. The correction data can also be incorporated at other in-linepoints in the data-path without departing from the scope of theinvention.

Correct Intensity Non-Uniformity in Data-Path

Each element in the array of individually controllable elements can beactivated to a state that depends on a control voltage. Where theelements in question consist of mirrors, the activation can take theform of a tilt about an axis in the plane of the mirror. The activationstate would then correspond to a particular angle of tilt. Theactivation state can also be referred to as a reflectivity set-point,for example, where elements of variable reflectivity (in a givendirection) are used in the array of individually controllable elements.The intensity of radiation in a sub-beam of radiation that has beenpatterned by one or more of these elements depends on the activationstate of the element(s) concerned. The conversion between an intensityand a control voltage can be implemented as a two-stage process. In afirst stage, a multiplication operation is performed to convertintensities to corresponding activation states (e.g., reflectivities).The second stage is then concerned with selecting appropriate controlvoltages in order to obtain these element activation states from thearray 104/204. The relationship between the control voltage and theresulting element activation state is not in general of a simple linearform, and a calibration table (e.g., look-up table) is normally providedto enable this conversion to be carried out. Interpolation can be usedto convert values lying between discrete points in the calibrationtable. Alternatively, a mathematical function (e.g., a Chebyshefpolynomial) can be fitted to all or a portion of the data in thecalibration table and conversion can be carried out using the resultingfitting function.

In one example, the overall conversion is carried out via“inverse-patterning-device” data manipulation device 514. This cancomprise a multiplier 516 (for performing stage 1 conversion—from spotintensity to element activation state or reflectivity set-point) and alookup table device 518 (for performing stage 2 conversion—from elementactivation state or reflectivity set-point to element control voltage),as discussed in reference to FIG. 5 above.

In one example, intensity non-uniformity can occur independently of theproperties of the array of individually controllable elements due to avariety of optical effects within the apparatus. The result can beunwanted intensity variations between individual spot exposures,individual optical columns, individual laser systems, etc. In principle,these variations can be taken into account by incorporating extracalibration information into the requested dose data sent along thedata-path. Although potentially effective for removing the intensityvariations, this kind of approach can result in an undesirable increasein the data-path internal dynamic intensity range to be able to cope.This can lead to an increase in costs.

In one example, the inverse-patterning-device data manipulation device514 is adapted to at least partially correct for intensitynon-uniformity. For example, calibration measurements can be used toestablish a new look-up table for device 518 that takes into account notonly the properties of the patterning device 104/204, but also factorscontributing to intensity non-uniformity. These calibration measurementscan be carried out in a fully assembled machine (i.e., where allintensity influencing factors are active). For example, the system canbe equipped with one or more dose sensors, both to measure the sourceintensity and the spot intensity. The ratio of the two quantities isrelated to the intensity non-uniformity. Furthermore, a spot sensor canbe included at substrate level that can measure the spot alignmentposition(s). Alternatively or additionally, substrate base techniquescan be used, which consist in printing a pattern (or an individual spot)and then deriving intensity non-uniformity characteristics using offlinetooling. Once the non-uniformity characteristics have been establishedstandard interpolation schemes can be used to calculate the new look-uptable values.

As an alternative to adjusting the lookup table values in device 518,intensity non-uniformity correction can be implemented by manipulatingproperties of the multiplier 516. For example, the gain (or gains) canbe varied to take account of non-uniformity effects.

Correcting for intensity non-uniformity at this late stage in thedata-path reduces the requirement for increased bandwidth/dynamic rangeat earlier stages in the data-path. This example can also help to reducerounding errors.

Avoid Performing Calculations for Values that are Either Totally Blackor White

In one example, an image processing algorithm, such as those performedby the inverse-optics device 512, performs matrix multiplications. Thehardware used to carry out these multiplications is specificallytailored to the type of calculation to be carried out, so it optimizedto achieve an optimal number of MACs (Multiply Accumulates) per second.The hardware in question (which can be a DSP or a more general CPU)comprises one or more FPGAs (Field Programmable Gate Arrays) with amultiplication section that can be built up from multiplication unitsspecially constructed to carry out MAC operations. Because the detailsof the image to be processed is not known in advance. The hardware isnormally designed to be able to cope with non-zero values at each of thegrid positions defining the image. This requires a large number of MACs,and therefore expensive hardware.

In lithographic applications, such as the inverse-optics device 512,most of the terms in the requested dose pattern vector [D] will be 0 or1 or, where grey tone imaging is used, 0 and 15, corresponding to theabsence or presence of a feature. The MAC operation for these can berelatively simple (e.g., no real multiplication is performed). In oneexample, the MAC either outputs a zero or a multiplication coefficient,which can be shifted a number of places to the left and padded withzeros at the least significant side. Only the edge regions of the deviceelements in the image consist of grey values for which a truemultiplication is performed. The black and white regions may not use thefull functionality provided by the multiplication units.

In one example, a dedicated pre-processor is provided in the FPGA beforethe multiplying stage, which is capable of identifying and handlingblack and white areas in the requested dose map. The multiplying sectionuses a reduced input consisting predominantly of the grey areas in therequested dose map, which may not use the full functionality of themultiplication units. This arrangement allows the number of MACs persecond (and therefore the cost) to be greatly reduced without having asignificant negative effect on the image processing performance.

FIG. 15 depicts a multiplication stage with a preprocessor 1500 forreducing calculation load, according to one embodiment of the presentinvention. As mentioned above, the pre-processor 1500 can also be formedas an integral part of the FPGA.

Ghost Light Suppression

In one example, ghost light can be produced, which is unwanted or straylight that manages to reach the substrate 114/214/314. This can arise,for example, via internal reflection within the system optics and/or viacross-talk between neighboring MLA spots. Optical elements of thelithographic apparatus are normally designed to avoid this as much aspossible, but it is extremely difficult to remove entirely.

In one example, using a direct least squares fit of the requested dosepattern to the array of spot exposures, ghost light can be corrected forby incorporating terms into the point-spread-function matrix [K]⁺. Inthe case where neighboring spot exposures can be imaging coherently, itis possible to correct for the stray light to a very high level. Whereneighboring spot exposures are exposed at different times, a lower levelcorrection can be achieved. This method does not use additional non-zeroterms in the matrix [K]⁺, which leads to additional multiplies andaccumulates in the data-path. This can result in a somewhat higher cost,but this can be offset on the one hand by potentially higher qualityimages or, on the other, by reduced costs in the optical system design(since less expense needs to be dedicated to avoiding ghost lightsuppression if it can be compensated).

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample only, and not limitation. It will be apparent to persons skilledin the relevant art that various changes in form and detail can be madetherein without departing from the spirit and scope of the invention.Thus, the breadth and scope of the present invention should not belimited by any of the above-described exemplary embodiments, but shouldbe defined only in accordance with the following claims and theirequivalents.

It is to be appreciated that the Detailed Description section, and notthe Summary and Abstract sections, is intended to be used to interpretthe claims. The Summary and Abstract sections can set forth one or more,but not all exemplary embodiments of the present invention ascontemplated by the inventor(s), and thus, are not intended to limit thepresent invention and the appended claims in any way.

What is claimed is:
 1. A system, comprising: a projection systemconfigured to project a beam of radiation onto a substrate as an arrayof sub-beams of radiation; a modulator configured to modulate thesub-beams of radiation to substantially form a requested dose pattern onthe substrate, the requested dose pattern being built up over time froman array of spot exposures, each of the spot exposures being produced byone of the sub-beams of radiation at a given time; a rasterizerconfigured to convert data defining the requested dose pattern to asequence of data representing the requested dose at a correspondingsequence of points within the pattern; a controller configured toreceive the sequence of data and generate a control signal therefrom,the control signal being used to control the modulator; and a focusdetermination unit configured to measure a position of at least aportion of the substrate relative to a plane of best focus, wherein thecontroller comprises a focus compensation unit, the focus compensationunit configured to change the control signal based on measureddeviations of the position of at least the portion of the substraterelative to the plane of best focus.
 2. The system of claim 1, whereinthe focus determination unit comprises: at least one ultrasonictransducer and receiver, rigidly connected to the projection system andconfigured to measure the position of the substrate surface relative tothe projection system, at one or more points, by measuring travel timeof reflected ultrasonic waves.
 3. The system of claim 1, wherein themodulator comprises an array of individually controllable elementsconfigured to provide the sub-beams of radiation.
 4. The system of claim1, wherein the modulator comprises an array of individually controllableelements configured to pattern the sub-beams of radiation.
 5. A method,comprising: projecting a beam of radiation onto a substrate as an arrayof sub-beams of radiation; modulating the sub-beams of radiation tosubstantially form a requested dose pattern on the substrate, therequested dose pattern being built up over time from an array of spotexposures, each of the spot exposures being produced by one of thesub-beams of radiation at a given time; converting data defining therequested dose pattern to a sequence of data representing the requesteddose at a corresponding sequence of points within the pattern;generating a control signal from the sequence of data that is used tocontrol the modulating; measuring the position of at least a portion ofthe substrate relative to a plane of best focus; and modifying thecontrol signal based on measured deviations of the position of at leasta portion of the substrate relative to the plane of best focus.
 6. Thesystem of claim 1, wherein the focus determination unit is furtherconfigured to output a coarse adjustment signal and focus data based onthe measured deviations of the position of at least the portion of thesubstrate relative to the plane of best focus.
 7. The system of claim 6,wherein the controller is further configured to receive the coarseadjustment signal and perform a coarse adjustment to at least one of aposition of the projection system and a position of a substrate table.8. The system of claim 6, wherein the focus compensation unit isconfigured to generate a fine adjustment signal based on the focus datato change the control signal.
 9. The system of claim 6, wherein thefocus compensation unit is configured to receive the coarse adjustmentsignal and generate a fine adjustment signal based on the focus data andthe coarse adjustment signal to change the control signal.
 10. Thesystem of claim 1, wherein the focus compensation unit is configured tochange the control signal substantially simultaneously with an exposureof the substrate by the array of sub-beams of radiation.
 11. The methodof claim 5, further comprising: generating a coarse adjustment signaland focus data based on the measured deviations of the position of atleast the portion of the substrate relative to the plane of best focus.12. The method of claim 11, further comprising: performing a coarseadjustment to at least one of a position of a projection system and aposition of a substrate table based on the coarse adjustment signal. 13.The method of claim 11, further comprising: generating a fine adjustmentsignal based on the focus data; wherein the modifying further compriseschanging the control signal based on the fine adjustment signal.
 14. Themethod of claim 11, further comprising: generating a fine adjustmentsignal based on the focus data and the coarse adjustment signal; whereinthe modifying further comprises changing the control signal based on thefine adjustment signal.
 15. The method of claim 5, wherein the modifyingfurther comprises: changing the control signal substantiallysimultaneously with an exposure of a substrate by the array of sub-beamsof radiation.
 16. A lithography apparatus, comprising: a patterningdevice configured to modulate a beam of radiation as an array ofsub-beams of radiation, the sub-beams of radiation substantially forminga requested dose pattern on a substrate; a projection system configuredto project the modulated sub-beams of radiation onto the substrate; afocus determination unit configured to measure a position of at least aportion of the substrate relative to a plane of best focus and output acoarse adjustment signal and focus data; a controller configured toreceive the coarse adjustment signal and perform a coarse adjustment toa position of the projection system and a position of a substrate tablebased on the coarse adjustment signal; a rasterizer configured toconvert data defining the requested dose pattern to a sequence of datarepresenting the requested dose at a corresponding sequence of pointswithin the pattern; a data path control device configured to: receivethe sequence of data and generate a control signal therefrom, thecontrol signal being used to control the patterning device; and receivethe focus data and generate a fine adjustment signal, the fineadjustment signal configured to change the control signal based onmeasured deviations of the position of at least a portion of thesubstrate relative to the plane of best focus.
 17. The lithographicapparatus of claim 16, wherein the requested dose pattern is built upover time from an array of spot exposures, each of the spot exposuresbeing produced by one of the sub-beams of radiation at a given time. 18.The lithographic apparatus of claim 16, wherein the patterning devicecomprises an array of individually controllable elements configured toprovide the sub-beams of radiation.
 19. The lithographic apparatus ofclaim 16, wherein the patterning device comprises an array ofindividually controllable elements configured to pattern the sub-beamsof radiation.
 20. The lithographic apparatus of claim 16, wherein thedata path control device is configured to change the control signalsubstantially simultaneously with an exposure of the substrate by thearray of sub-beams of radiation.